This invention relates to a method and apparatus for simulating a mechanical operation and, in particular, to an operation in the forming industries.
In such molding industries, a shape of a material, a die and a manufacturing process must be carefully designed in order to improve a quality of a product and to reduce a cost.
Heretofore, ordinary simulation apparatuses have been used to analyze a flow and deformation process of a material for the purpose of prediction in product design. For example, a conventional analyzing method is disclosed in a paper written by Manabu Goto and Tomotsugu Shibuya and contributed to The Proceeding of the 1989 Japanese Spring Conference for the Technology of Plasticity under the title of "Finite Element Analysis on Elastoplasticity in Die Forging of a Gear Material". Specifically, let a product illustrated in FIG. 1 be deformed by the use of a die D and a material M illustrated in FIG. 2. The material M alone is divided or meshed into a plurality of divided elements or finite element meshes as shown in FIG. 2. Simulation is carried out by predicting changes of the divided elements which might occur during a forming operation. Results of the simulation is illustrated in FIGS. 3(a) through 3(d). In FIGS. 3(a) through 3(d), the die D is assumed to be moved from an initial state (FIG. 3(a)) to a final state (FIG. 3(d)) at strokes of 6.0 mm, 12.0 mm, 13.5 mm, and 15 mm, respectively. As is apparent from FIG. 3(c), re-division or remeshing should be done in connection with the divided elements, as depicted by solid lines. This means that the divided elements are undesirably deformed during the forming operation.
Specifically, the above-mentioned conventional method is carried out on the basis of a "finite element" program which includes an additional step in consideration of a predetermined boundary condition and remeshing. Thus, a basic forming operation is analyzed by the deformation finite elements by considering states before and after deformation, as shown in FIG. 4. In this event, a flow and deformation process of a material is numerically simulated in accordance with the finite element program by modelling the material alone of both the material and the die by the use of finite elements and by tracing the deformation of the finite elements themselves.
However, the conventional method should consider and evaluate a contact boundary between the die and the material as suggested in FIG. 5. This inevitably results in a calculation error because such evaluation of a contact is very difficult.
More particularly, the finite elements per se are deformed in the conventional method as mentioned above. With the progress of deformation, the finite elements are so extensively distorted or deformed as shown in FIG. 6. This makes further calculation impossible. In order to cope with such an excessive deformation, the above-mentioned remeshing should be repeated at every time when the excessive deformation takes place. However, the remeshing is extremely troublesome for a user.